What is the dot product of complex conjugate vectors?

[janu203]

what is the dot product of two complex conjugate vectors?

 

[Simon Bridge]

$$\vec v^\star \cdot \vec v $$ you mean?
You can figure it out for yourself...

So let $\vec v = (v_1,v_2,v_3,\cdots)^t$ And $\vec u = (u_1,u_2,u_3,\cdots)^t$ where $v_i,u_i\in\mathbb{C}$

What would $\vec u \cdot \vec v$ be, in terms of the components?

Now let $\vec u = \vec v^\star$

 

[janu203]

sorry sir! i didn't get you

 

[Simon Bridge]

Use the algebraic definition of the dot product.